We all know, that Double Jeopardy applies in the US, stopping one from getting tried twice for the same act... by the same type of court. Double Jeopardy does obviously not apply to being tried by the state and the federal court system, where you can be convicted for drug smuggling by both the Federal and the State court as you broke both laws with the same act. Sometimes one of them is using the result of the other as evidence and to fast track the trial.
With the right setup, we know that up to 4 states, 2 tribal governments, and the federal court system could get you for murder on the Four Corner's Monument.
How would being in the US Military add to that? Could a military court take the same act (in the example murder, but possibly also noncapital crimes) and try you for the same or different charge to further increase the punishment?